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NP Complete
In computational complexity theory, NP-complete problems are the hardest of the problems to which ''solutions'' can be verified ''quickly''. Somewhat more precisely, a problem is NP-complete when: # It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". # When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) ''solution''. # The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # The problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. Hence, if we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3SAT 17 Svg
3sat (, ''Dreisat'') is a free-to-air German-language public service television channel. It is a generalist channel with a cultural focus and is jointly operated by Public broadcasting, public broadcasters from Germany (ZDF, ARD (broadcaster), ARD), Austria (ORF (broadcaster), ORF) and Switzerland (SRG SSR). The coordinating broadcaster is ZDF, at whose Mainz facility the broadcasting centre with studios for in-house productions is located. History 3sat was established to broadcast high culture, cultural programmes, originally by satellite. The network was founded as a cooperative network by Germany's ZDF, Austria's ORF (broadcaster), ORF, and Switzerland's SRG SSR (formerly SRG SSR idée suisse). 3sat began broadcasting on 1 December 1984, with its first programme being simulcasted on ORF 2, FS2, SRF 1, TV DRS and ZDF. ZDF leads the cooperative, though decisions are reached through consensus of the cooperative's partners. In 1990, Deutscher Fernsehfunk, DFF, television broadc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heuristic (computer Science)
A heuristic or heuristic technique (''problem solving'', ''Heuristic (psychology), mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a Pragmatism, pragmatic method that is not fully Mathematical optimisation, optimized, perfected, or Rationality, rationalized, but is nevertheless "good enough" as an approximation or attribute substitution. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of Decision-making, making a decision. Context Gigerenzer & Gaissmaier (2011) state that Set (mathematics), sub-sets of ''strategy'' include heuristics, regression analysis, and Bayesian inference. Heuristics are strategies based on rules to generate optimal decisions, like the anchoring effect and utility maximization problem. These strategies depend on using readily accessible, thoug ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unsolved Problems Of Mathematics
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations. Some problems belong to more than one discipline and are studied using techniques from different areas. Prizes are often awarded for the solution to a long-standing problem, and some lists of unsolved problems, such as the Millennium Prize Problems, receive considerable attention. This list is a composite of notable unsolved problems mentioned in previously published lists, including but not limited to lists considered authoritative, and the problems listed here vary widely in both difficulty and importance. Lists of unsolved problems in mathematics Various mathematicians and organiza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Hopcroft
John Edward Hopcroft (born October 7, 1939) is an American theoretical computer scientist. His textbooks on theory of computation (also known as the Cinderella book) and data structures are regarded as standards in their fields. He is a professor emeritus at Cornell University, co-director of the Center on Frontiers of Computing Studies at Peking University, and the director of the John Hopcroft Center for Computer Science at Shanghai Jiao Tong University. Early life and education Hopcroft received a Bachelor of Science with a major in electrical engineering from Seattle University in 1961. He received a Master of Science in electrical engineering in 1962 and a Doctor of Philosophy in electrical engineering in 1964, both from Stanford University. Hopcroft is the grandson of Jacob Nist, who established the Seattle-Tacoma Box Company in 1889. Career and honor He worked for three years at Princeton University and since then has been at Cornell University. In addition to his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete mathematics, discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the Alphabet (formal languages), alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write, which direction to move the head, and whet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deterministic
Determinism is the metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. Like eternalism, determinism focuses on particular events rather than the future as a concept. Determinism is often contrasted with free will, although some philosophers claim that the two are compatible. A more extreme antonym of determinism is indeterminism, or the view that events are not deterministically caused but rather occur due to random chance. Historically, debates about determinism have involved many philosophical positions and given rise to multiple varieties or interpretations of determinism. One topic of debate concerns the scope of determined systems. Some philosophers have maintained that the entire universe is a single determinate system, while others identify more limited determinate systems. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symposium On Theory Of Computing
The Annual ACM Symposium on Theory of Computing (STOC) is an academic conference in the field of theoretical computer science. STOC has been organized annually since 1969, typically in May or June; the conference is sponsored by the Association for Computing Machinery special interest group SIGACT. Acceptance rate of STOC, averaged from 1970 to 2012, is 31%, with the rate of 29% in 2012. As writes, STOC and its annual IEEE counterpart FOCS (the Symposium on Foundations of Computer Science) are considered the two top conferences in theoretical computer science, considered broadly: they “are forums for some of the best work throughout theory of computing that promote breadth among theory of computing researchers and help to keep the community together.” includes regular attendance at STOC and FOCS as one of several defining characteristics of theoretical computer scientists. Awards The Gödel Prize for outstanding papers in theoretical computer science is presented alternate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cook–Levin Theorem
In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-completeness, NP-complete. That is, it is in NP (complexity), NP, and any problem in NP can be reduction (complexity), reduced in polynomial time by a deterministic Turing machine to the Boolean satisfiability problem. The theorem is named after Stephen Cook and Leonid Levin. The proof is due to Richard Karp, based on an earlier proof (using a different notion of reducibility) by Cook. An important consequence of this theorem is that if there exists a deterministic polynomial-time algorithm for solving Boolean satisfiability, then every NP (complexity), NP problem can be solved by a deterministic polynomial-time algorithm. The question of whether such an algorithm for Boolean satisfiability exists is thus equivalent to the P versus NP problem, which is still widely considered the most important unsolved problem in theoretical computer sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P Np Np-complete Np-hard
P, or p, is the sixteenth letter (alphabet), letter of the Latin alphabet, used in the English alphabet, modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is English alphabet#Letter names, ''pee'' (pronounced ), plural ''pees''. History The Semitic languages, Semitic Pê (mouth), as well as the Greek language, Greek Π or π (Pi (letter), Pi), and the Etruscan language, Etruscan and Latin letters that developed from the former alphabet all symbolized , a voiceless bilabial plosive. Use in writing systems English In English orthography, represents the sound . A common Digraph (orthography), digraph in English is , which represents the sound , and can be used to transliterate ''phi'' in loanwords from Greek language, Greek. In German, the digraph is common, representing a labial affricate . Most English words beginning with are of foreign origin, primarily French, Latin and Greek; these languages pres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Machine
In computer science, an abstract machine is a theoretical model that allows for a detailed and precise analysis of how a computer system functions. It is similar to a mathematical function in that it receives inputs and produces outputs based on predefined rules. Abstract machines vary from literal machines in that they are expected to perform correctly and independently of hardware. Abstract machines are "machines" because they allow step-by-step execution of programs; they are " abstract" because they ignore many aspects of actual ( hardware) machines. A typical abstract machine consists of a definition in terms of input, output, and the set of allowable operations used to turn the former into the latter. They can be used for purely theoretical reasons as well as models for real-world computer systems. In the theory of computation, abstract machines are often used in thought experiments regarding computability or to analyse the complexity of algorithms. This use of abstract mac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Completeness
In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician and computer scientist Alan Turing). This means that this system is able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. A related concept is that of Turing equivalence two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Turing Machine
In computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Common sense might say that a universal machine is impossible, but Turing proves that it is possible. He suggested that we may compare a human in the process of computing a real number to a machine which is only capable of a finite number of conditions ; which will be called "-configurations". He then described the operation of such machine, as described below, and argued: Turing introduced the idea of such a machine in 1936–1937. Introduction Martin Davis makes a persuasive argument that Turing's conception of what is now known as "the stored-program computer", of placing the "action table"—the instructions for the machine—in the same "memory" as the input data, strongly influenced John von Neumann's conception of the first Amer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
